Let `a ,ba n dc` be real numbers such that `a+2b+c=4` . Find the maximum value of `(a b+b c+c a)dot`

Let a,b,c be real numbers such that a+2b+c=4. Find max(ab+bc+ca)

If a,b,c are positive real numbers such that a +b+c=18, find the maximum value of a^(2)b^(3)c^(4)

Let a,b,c,d he real numbers such that a+b+c+d=10, then the minimum value of ^(2)cot9^(@)-b^(2)cot27^(@)+c^(2)cot63^(@)+d^(2)cot81^(@) is sqrt(n),(n in N) find n.

Let a,b and c be real numbers such that 4a+2b+c=0 and ab<0. Then the equation ax^(2)+bx+c=0

Let a,b and c be positive real numbers such that a+b+c=6. Then range of ab^(2)c^(3) is